Version 5.0 The LEDA User Manual

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• internal (LEDA/incl/internal/) Module internal contains include files that are needed for LEDA’s maintenance or for people who want to implement extension packages. • beta (LEDA/incl/beta/) Module beta contains data types that are not fully tested. We will still maintain the old include structure for a fixed period of time. Please note that we will however turn off the old include structure in one of the next releases. The old include structure is available under $(LEDAROOT)/incl old/LEDA/.
Chapter 4 Simple Data Types and Basic Support Operations This section describes simple data types like strings, streams and gives some information about error handling, memory management and file system access. The stream data types described in this section are all derived from the C++ stream types istream and ostream. They can be used in any program that includes the header file. Some of these types may be obsolete in combination with the latest versions of the standard C++ I/O library. 4.1 Strings ( string ) 1. Definition An instance s of the data type string is a sequence of characters (type char). The number of characters in the sequence is called the length of s. A string of length zero is called the empty string. Strings can be used wherever a C++ const char∗ string can be used. Strings differ from the C++ type char∗ in several aspects: parameter passing by value and assignment works properly (i.e., the value is passed or assigned and not a pointer to the value) and strings offer many additional operations. #include < LEDA/core/string.h > 2. Types string :: size type the size type. 3. Creation string s; introduces a variable s of type string. s is initialized with the empty string. 23
Page 1: Version 5.0 The LEDA User Manual Al
Page 4 and 5: 4.14 Socket Streambuffer ( socket s
Page 6 and 7: 9.11 Move-To-Front Coder II ( MTF2C
Page 8 and 9: 13.1.2 Handles and Iterators . . .
Page 10 and 11: 16.7 Simplices in 3D-Space ( d3 sim
Page 13: License Terms and Availability Any
Page 16 and 17: 7. LEDA is available from Algorithm
Page 19 and 20: Chapter 2 Basics An extended versio
Page 21 and 22: XYZ y(x1, ... ,xt); ,tk > and uses
Page 23 and 24: 2.3.1 Linear Orders Many data types
Page 25 and 26: dictionary D0; // default ordering
Page 27 and 28: 2.3.3 Implementation Parameters Man
Page 29 and 30: lookup returned the location where
Page 31: list::iterator defines the iterator
Page 36 and 37: string s(const char ∗ p); string
Page 38 and 39: ool bool bool bool istream& ostream
Page 40 and 41: string buffer, i.e., all output ope
Page 42 and 43: andom source& S ≫ char& x random
Page 44 and 45: int R.set weight(int i, int g) sets
Page 46 and 47: 4.10 Memory Allocator ( leda alloca
Page 48 and 49: 4.11 Error Handling ( error ) LEDA
Page 50 and 51: 4.12 Files and Directories ( file )
Page 52 and 53: 4.13 Sockets ( leda socket ) 1. Def
Page 54 and 55: ool S.receive string(string& s) rec
Page 56 and 57: ool sb.failed( ) returns whether a
Page 58 and 59: 4.15 Some Useful Functions ( misc )
Page 60 and 61: 4.16 Timer ( timer ) 1. Definition
Page 62 and 63: unsigned fibonacci(unsigned n) { st
Page 64 and 65: unsigned fibonacci(unsigned n) { st
Page 66 and 67: int Hash(const two tuple& p) hash f
Page 68 and 69: 3. Creation four tuple p; creates a
Page 70 and 71: 4.21 A date interface ( date ) 1. D
Page 72 and 73: 3. Creation date D; creates an inst
Page 74 and 75: string D.get month name( ) returns
Page 76 and 77: Now we show an example in which dif
Page 78 and 79: integer integer a(const char ∗ s)
Page 80 and 81: 5.2 Rational Numbers ( rational ) 1
Page 82 and 83: 5.3 The data type bigfloat ( bigflo
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ounding modes bigfloat :: get round
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ostream& ostream& os ≪ const bigf
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double x.get double error( ) bigflo
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int int real roots(const Polynomial
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√ y v = b 1 c 2 + b 2 c 1 ± sign
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5.5 Interval Arithmetic in LEDA ( i
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void x.set midpoint(VOLATILE I doub
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5.7 The mod kernel of type residual
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int residual :: required primetable
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5.9 A Floating Point Filter ( float
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5.10 Double-Valued Vectors ( vector
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double v.zcoord( ) returns the seco
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matrix matrix matrix vector M + con
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5.12 Vectors with Integer Entries (
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5.13 Matrices with Integer Entries
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integer matrix inverse(const intege
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distinct representatives and linear
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at vector v(const array& A); introd
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int compare by angle(const rat vect
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5.15 Real-Valued Vectors ( real vec
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int compare by angle(const real vec
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eal matrix M + const real matrix& M
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5.17.2 Integration double integrate
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array A(int low, const E& x, const
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int A.binary locate(int (∗cmp)(co
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6.3 Stacks ( stack ) 1. Definition
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6.5 Bounded Stacks ( b stack ) 1. D
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6.7 Linear Lists ( list ) 1. Defini
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const E& L.pop front( ) same as L.p
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Sorting and Searching void L.sort(i
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Input and Output void L.read(istrea
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6.8 Singly Linked Lists ( slist ) 1
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6.9 Sets ( set ) 1. Definition An i
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4. Implementation Sets are implemen
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int set S | const int set& T return
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d int set S − const d int set& T
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6.12 Partitions ( partition ) 1. De
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6.13 Parameterized Partitions ( Par
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void D.evert(vertex v) makes v the
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4. Implementation Dynamic collectio
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dictionary D(int (∗cmp)(const K&
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7.2 Dictionary Arrays ( d array ) 1
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{ d_array dic; dic["hello"] = "hall
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ool A.empty( ) returns true if A is
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Note that it is not possible to ite
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void M.clear( ) clears M by making
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p dictionary D.change inf(p dic ite
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void D.del(const K& k) deletes the
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3. Creation sortseq S; creates an i
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seq item S.max item( ) returns the
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Iteration forall items(it, S) { “
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Chapter 8 Priority Queues 8.1 Prior
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6. Example Dijkstra’s Algorithm (
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int Q.size( ) returns the size of Q
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Assume that you want to send the fi
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9.1 Adaptive Arithmetic Coder ( A0C
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uint32 C.get scale threshold( ) uin
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uint32 C.decode memory chunk(const
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3. Creation PPMIICoder C(streambuf
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9.4 Deflation/Inflation Coder ( Def
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void C.set compression level(int le
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void void C.set src stream(streambu
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streambuf ∗ C.get src stream( ) r
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streambuf ∗ C.get src stream( ) r
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uint32 C.decode memory chunk(const
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uint32 C.encode memory chunk(const
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9.10 Move-To-Front Coder ( MTFCoder
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9.11 Move-To-Front Coder II ( MTF2C
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9.12 RLE for Runs of Zero ( RLE0Cod
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9.13 Checksummers ( checksummer bas
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ool C.checksum is valid( ) returns
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9.19 Encoding Output Stream ( encod
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ostream& os.seekp(streamoff off , i
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9.23 Coder Pipes ( CoderPipe2 ) 1.
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void C.set coder1(Coder1 ∗ c1 , b
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void void C.set src stream(streambu
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3. Operations Standard Operations v
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string out_file1 = tmp_file_name(),
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void mb.truncate(streamsize n) also
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e able to change your message witho
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Then you can use the CryptAutoDecod
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10.1 Secure Byte String ( CryptByte
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CryptKey k(const byte ∗ bytes, ui
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10.3 Encryption and Decryption with
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10.4 Example for a Stream-Cipher (
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uint16 void C.get accepted key size
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3. Operations Standard Operations v
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10.6 Automatic Decoder supporting C
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void C.add keys in file(const char
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secure socket streambuf sb(leda soc
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Chapter 11 Graphs and Related Data
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2. Creation graph G; creates an obj
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edge G.first in edge(node v) return
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void G.hide node(node v) removes no
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void G.bucket sort nodes(int l, int
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edge G.new map edge(edge e1 , edge
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edge edge edge G.new edge(node v, e
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void void G.print(string s, ostream
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graph algorithms, i.e., algorithms
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void void G.sort nodes(const list&
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• Opposite Graphs (opposite graph
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4. Operations The interface consist
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int main () { static_graph G; array
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3. Implementation see section 11.2.
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list M.triangulate( ) triangulates
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void M.assign(face f, const ftype&
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void A.init(const graph t& G, int n
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ool M.use node data(const graph t&
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ool M.use edge data(const graph t&
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E& M[face f] returns the variable M
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4. Implementation Node matrices for
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4. Implementation Node maps are imp
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11.17 Sets of Edges ( edge set ) 1.
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node L.cyclic pred(node v) returns
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11.20 Node Priority Queues ( node p
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11.21 Bounded Node Priority Queues
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11.22 Graph Generators ( graph gen
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uedges. For n > 3, a random maximal
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void random planar graph(graph& G,
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ool Is Bidirected(const graph& G) r
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list Delete Loops(graph& G) returns
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11.25 Dynamic Markov Chains ( dynam
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has a source and a target. These ar
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void parser.append(const char ∗ k
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11.27 The LEDA graph input/output f
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arithmetic demand for each function
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GRAPH TRANSITIVE CLOSURE(const gra
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template bool SHORTEST PATH T(cons
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template bool ALL PAIRS SHORTEST P
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The algorithms have the following a
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inline NT MAX FLOW GRH T(const grap
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12.5 Minimum Cut ( min cut ) A cut
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that the bipartition (A, B) is give
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The pre-instantiations for number t
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template bool CHECK MIN WEIGHT ASS
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in general graph. You may skip the
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Worst-Case Running Time: All functi
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list MIN WEIGHT PERFECT MATCHING T(
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12.10 Stable Matching ( stable matc
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12.11 Minimum Spanning Trees ( min
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12.13 Algorithms for Planar Graphs
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ool bool Is CCW Ordered(const graph
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ool void void void TUTTE EMBEDDING(
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Chapter 13 Graphs and Iterators 13.
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The purpose of each iterator is the
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template void set_and_check (graph
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In addition to the algorithm mentio
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13.3 Edge Iterators ( EdgeIt ) 1. D
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#include < LEDA/graph/graph iterato
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OutAdjIt OutAdjIt OutAdjIt it(const
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OutAdjIt& −−it performs one ste
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ool it.eol( ) returns !it.valid( )
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void it.del( ) deletes the marked l
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3. Operations void fc.init(const le
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We would have to write something li
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Equal is a class that compares two
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used only as a “Trojan horse,”
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typename DataAccessor :: value type
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13.14 Constant Accessors ( constant
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13.16 Node Attribute Accessors ( no
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GIT BFS< OutAdjIt, Queuetype, Mark
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3. dfs grow depth: a new adjacency
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• indegree stores for every node
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• Mark is a data accessor that ha
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OutAdjIt algorithm.curr adj( ) retu
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14.1 Points ( point ) 1. Definition
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point p.reflect(const point& q, con
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ool contained in simplex(const arra
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4. Operations point s.start( ) retu
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segment s.rotate90(const point& q,
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double r.direction( ) returns the d
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14.4 Straight Lines ( line ) 1. Def
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line l.translate(const vector& v) r
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14.5 Circles ( circle ) 1. Definiti
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circle C + const vector& v returns
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14.6 Polygons ( POLYGON ) 1. Defini
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const list& P.segments( ) returns t
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ool P.inside(const POINT & p) bool
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14.7 Generalized Polygons ( GEN POL
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GEN POLYGON GEN POLYGON :: make wea
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int P.side of(const POINT & p) regi
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14.8 Triangles ( triangle ) 1. Defi
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triangle t.rotate90(const point& q,
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double r.height( ) returns the heig
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14.10 Rational Points ( rat point )
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at point p.reflect(const rat point&
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int side of halfspace(const rat poi
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at segment s(const segment& s1 , in
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ational s.y abs( ) returns the y-ab
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14.12 Rational Rays ( rat ray ) 1.
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ool r.contains(const rat segment& s
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void l.normalize( ) simplifies the
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at line p bisector(const rat point&
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at circle C(const circle& c, int pr
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14.15 Rational Triangles ( rat tria
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at triangle t − const rat vector&
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list r.vertices( ) returns the vert
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list r.intersection(const rat recta
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int p.orientation(const real point&
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eal area(const real point& a, const
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14.18 Real Segments ( real segment
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ool s.intersection(const real segme
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14.19 Real Rays ( real ray ) 1. Def
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Non-Member Functions int orientatio
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4. Operations real point l.point1(
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int cmp slopes(const real line& l1
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eal circle C(const circle& c, int p
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ool radical axis(const real circle&
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eal point t.point3( ) returns the t
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14.23 Iso-oriented Real Rectangles
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eal rectangle r.translate(real dx,
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14.24 Geometry Algorithms ( geo alg
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edge TRIANGULATE PLANE MAP(GRAPH &
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gen polygon MINKOWSKI SUM(const pol
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ool MIN WIDTH ANNULUS(const list& L
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double CLOSEST PAIR(list& L, point&
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14.25 Transformation ( TRANSFORM )
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TRANSFORM reflection(const POINT& q
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void random points in unit cube(int
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void random points on unit circle(i
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const rat point& p.to rat point( )
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circle segment cs(const rat circle&
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list cs.intersection(const r circle
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14.29 Polygons with circular edges
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CHECK TYPE P.check simplicity( ) ch
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ool P.inside(const r circle point&
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circle gen polygon P (KIND k); crea
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list P.intersection(const rat line&
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double P.approximate area( ) approx
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const I& D.inf(dic2 item it) return
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15.2 Point Sets and Delaunay Triang
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ool T.is hull edge(edge e) as above
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list T.range search(node v, const P
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15.3 Sets of Intervals ( interval s
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15.4 Sets of Parallel Segments ( se
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15.5 Sets of Parallel Rational Segm
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15.6 Planar Subdivisions ( subdivis
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16.1 Points in 3D-Space ( d3 point
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d3 point midpoint(const d3 point& a
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ool outside sphere(const d3 point&
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ool bool r.project xz(ray& m) if th
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segment s.project xy( ) returns the
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ool l.project(const d3 point& p, co
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double p.sqr dist(const d3 point& q
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16.6 Spheres in 3D-Space ( d3 spher
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16.7 Simplices in 3D-Space ( d3 sim
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16.8 Rational Points in 3D-Space (
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d3 rat point p.translate(const rat
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ool coplanar(const d3 rat point& a,
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d3 rat point random d3 rat point in
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void random d3 rat points on segmen
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ool r.project xy(rat ray& m) bool r
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ool l.project yz(rat line& m) if th
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16.11 Rational Segments in 3D-Space
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d3 rat segment s + const rat vector
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d3 plane p.to float( ) returns a fl
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16.13 Rational Spheres ( d3 rat sph
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16.14 Rational Simplices ( d3 rat s
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16.15 3D Convex Hull Algorithms ( d
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Chapter 17 Graphics This section de
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17.2 Windows ( window ) 1. Definiti
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18. The buttons per line parameter
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void W.display(window& W 0 , int x,
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void W.set show coord object(const
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int W.menu bar height( ) returns th
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void W.draw ray(point p, point q, l
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void W.draw filled ellipse(double x
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void void void void void W.draw rou
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void void void W.draw edge(double x
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void W.screenshot(string fname, boo
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int W.read mouse seg(const point& p
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int W.read event(int& val, double&
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window& W ≫ segment& s reads a se
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panel item W.bool item(string s, bo
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panel item W.int item(string s, int
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int W.button(string s, const char
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int W.button(string s, window& M, c
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void void void W.redraw panel(panel
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17.4 Menues ( menu ) 1. Definition
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17.5 Postscript Files ( ps file ) 1
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shape: the shape of the node (type
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void gw.display(int x, int y) displ
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param type gw.set param(node v, par
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string gw.set edge index format(str
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void void gw.transform layout(node
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int bool bool gw.load layout(istrea
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void void gw.set edge slider handle
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int bool bool bool bool bool bool g
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void gw.restore all attributes( ) .
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6. edge index format format This li
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of GraphWin) are 0 (central pos) 1
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17.7.1 A complete example LEDA.GRAP
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17.8 Geometry Windows ( GeoWin ) 1.
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0 will be drawn on top in the order
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geowin new scene and geowin get obj
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e inserted in the result scene. In
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geo_scene sc_points = gw.new_scene(
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} }; int main() { GeoWin gw; list L
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virtual bool is_running(const GeoWi
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geo scene void int GW.get scene wit
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color GW.get fill color(geo scene s
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void∗ GW.set client data(geo scen
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color GW.set obj color(GeoBaseScene
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template string GW.set obj label(G
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string string GW.get bg pixmap( ) r
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• A DRAG (button not released)
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template bool GW.set post del hand
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geowin_gui_rat_transform geowin_gui
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ool GW.del(geo scenegroup GS , geo
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void GW.set d3 fcn(geo scene sc, vo
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17.9 Windows for 3d visualization (
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int D.move( ) animates the contents
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Chapter 18 Implementations 18.1 Lis
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void clear(); int size() const; };
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18.2.3 Sorted Sequences Any class s
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libGeoW is the LEDA library providi
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(b) Type VCVARS32 (VSVARS32). 2. Go
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LEDA MEMORY STD: If this is set, th
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When using graphics on Solaris syst
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(7) Double click on prog.cpp If you
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• extend LIB by Otherwise add ne
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and at least one of the following d
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• Copy leda .dll to the bin\ subd
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Preparations To install LEDA you on
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• libg .lib libl .lib for program
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cl -TP prog.c Programs using grap
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Automatic Setting Include header fi
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The default value is ”/MLd”, al
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2. Windows 95/98: (a) Add the line
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Preparations To install LEDA you on
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A.16 Platforms When this manual was
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(b) For objects x and y of an indep
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A and B are different objects: A ==
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if (p.y > q.y) return 1; return 0;
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partypes={no, yes} Determines how p
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Stacks ( stack ) 1. Definition An i
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Bibliography [1] H. Alt, N. Blum, K
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[31] I. Fary: “On Straight Line R
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[67] M. Mignotte: Mathematics for C
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Index Symbols L A TEX . . . . . . .
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adj nodes(...) graph . . . . . . .
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circle gen polygon . . . . . . . .
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at ray . . . . . . . . . . . . . .
Page 783 and 784:
CBCCoder< BlkCipher > . . . . . . .
Page 785 and 786:
disconnect() leda socket . . . . .
Page 787 and 788:
edges() GEN POLYGON . . . . . . . .
Page 789 and 790:
finger locate pre...(...) sortseq .
Page 791 and 792:
checksummer base . . . . . . . . .
Page 793 and 794:
OMACCoder< BlkCipher > . . . . . .
Page 795 and 796:
get stack() GIT DFS . . . . . . . .
Page 797 and 798:
in pred(...) graph . . . . . . . .
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eal triangle . . . . . . . . . . .
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at segment . . . . . . . . . . . .
Page 803 and 804:
eal rectangle . . . . . . . . . . .
Page 805 and 806:
mw matching . . . . . . . . . . . .
Page 807 and 808:
outdeg(...) graph . . . . . . . . .
Page 809 and 810:
pos(...) POINT SET . . . . . . . .
Page 811 and 812:
eal matrix . . . . . . . . . . . .
Page 813 and 814:
FaceIt . . . . . . . . . . . . . .
Page 815 and 816:
save gw(...) GraphWin . . . . . . .
Page 817 and 818:
set edge index fo...(...) GraphWin
Page 819 and 820:
GeoWin . . . . . . . . . . . . . .
Page 821 and 822:
DeflateCoder . . . . . . . . . . .
Page 823 and 824:
planar map . . . . . . . . . . . .
Page 825 and 826:
d3 rat point . . . . . . . . . . .
Page 827 and 828:
GraphWin . . . . . . . . . . . . .
Page 829 and 830:
at segment . . . . . . . . . . . .
show all

Version 5.0 The LEDA User Manual

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